What if it's a pretty significant rev jump: from 6th to 4th or even to 3rd maybe? Will the internal synchro's still be fine?

From that M5 training vid, the guy seemed to agree with you that you really don't NEED to double-clutch in normal down shifting, but he did seem to imply that there was some minor benefit.

Dare I say it but if you suddenly need to shift from 6th to 4th you probably haven't been reading the road right. If you're looking to overtake then you should be in the right gear before you move out which might, in your example, have been 5th.